hi everyone, I have posted many queries regarding implementation of MUSIC algorithm in MATLAB. Now I have written a program that estimates the DOA using music algorithm. There are some queries and doubts about the results I got from the output which I would like to share. Let N be the no of sensors and M be the number of signals incident on the sensors. When I do the SVD of the auto correlation matrix, I am supposed to get (N-M) number of eigen values which are equal to the variance of noise vector. I am getting very small values which is in concurrence with the theory but I am not getting the same values. The noise eigen values are decreasing. Also the value of the first eigen value of the signal subspace is relatively very large than the rest of the eigen values of the signal subspace. Is there an error in my program? Also every time I execute the program, the peaks are varying enormously for the various DOA signals. sometimes some peaks in the plots are very low except the peak corresponding to the first eigen vector. I plotted the spectrum (doa spectrum) from -90 to +90 degrees. When i try to include a DOA nearer to the boundary (-80 to -90) and (+80 - +90), they are invariably damped. Can anyone explain the reason for this behaviour? Thank you.

# doubt

Started by ●September 14, 2008

Reply by ●September 19, 20082008-09-19

On Sep 14, 12:54 am, "krish_dsp" <nmkr...@gmail.com> wrote:> hi everyone, > I have posted many queries regarding implementation of MUSIC algorithm in > MATLAB. Now I have written a program that estimates the DOA using music > algorithm. > There are some queries and doubts about the results I got from the output > which I would like to share. > Let N be the no of sensors and M be the number of signals incident on the > sensors. > When I do the SVD of the auto correlation matrix, I am supposed to get > (N-M) number of eigen values which are equal to the variance of noise > vector. I am getting very small values which is in concurrence with the > theory but I am not getting the same values. The noise eigen values are > decreasing. Also the value of the first eigen value of the signal subspace > is relatively very large than the rest of the eigen values of the signal > subspace. > Is there an error in my program? > Also every time I execute the program, the peaks are varying enormously > for the various DOA signals. sometimes some peaks in the plots are very low > except the peak corresponding to the first eigen vector. > > I plotted the spectrum (doa spectrum) from -90 to +90 degrees. When i try > to include a DOA nearer to the boundary (-80 to -90) and (+80 - +90), they > are invariably damped. Can anyone explain the reason for this behaviour? > > Thank you.It's hard to answer your questions without understanding what algorithm your code is implementing. Can you describe the formulae that you are implementing? Then, we should be able to help you. Thanks, Dilip.

Reply by ●September 19, 20082008-09-19

On 14 Sep, 06:54, "krish_dsp" <nmkr...@gmail.com> wrote:> hi everyone, > I have posted many queries regarding implementation of MUSIC algorithm in > MATLAB. Now I have written a program that estimates the DOA using music > algorithm. > There are some queries and doubts about the results I got from the output > which I would like to share. > Let N be the no of sensors and M be the number of signals incident on the > sensors. > When I do the SVD of the auto correlation matrix, I am supposed to get > (N-M) number of eigen values which are equal to the variance of noise > vector.That happens only if the number of signals is indeed smaller than the number of sensors.> I am getting very small values which is in concurrence with the > theory but I am not getting the same values.Who said you would get the same values?> The noise eigen values are > decreasing. Also the value of the first eigen value of the signal subspace > is relatively very large than the rest of the eigen values of the signal > subspace.Is there a reason why it shouldn't?> Is there an error in my program?I have no idea. What you have described so far is more or less to be expected.> Also every time I execute the program, the peaks are varying enormously > for the various DOA signals. sometimes some peaks in the plots are very low > except the peak corresponding to the first eigen vector.Where did you get those peaks from?> I plotted the spectrum (doa spectrum) from -90 to +90 degrees. When i try > to include a DOA nearer to the boundary (-80 to -90) and (+80 - +90), they > are invariably damped. Can anyone explain the reason for this behaviour?MUSIC computes no peaks. Whatever it is you plot, it is random data that are unrelated to anything useful in the signal. Rune

Reply by ●September 19, 20082008-09-19

hi.. i will talk about the eigen values first. When I read the theory of MUSIC vectors, it was given that (in the form of expression) that out of the N eigen values we get, first M (no of signals) eigen values will be equal to the sum of the variance of noise and the eigen value of signals, then the remaining (N-M) eigen values will be equal to the variance of the noise. So all the N-M values should be equal isn't it. B'cos the auto correlation of the noise results in (sigma)^2 * I(identity matrix). If its not clear, I can share my program as a followup message. may be I am not explaining the things well. As u said the MUSIC doesn't compute any peaks. But for visual representation of the working of the algorithm, i plotted the result. for more clarification I can send the code. The MUSIC algorithm is not good for coherent signals. What are the algorithms that are good in DOA estimation for coherent signals. bye.>On 14 Sep, 06:54, "krish_dsp" <nmkr...@gmail.com> wrote: >> hi everyone, >> I have posted many queries regarding implementation of MUSIC algorithmin>> MATLAB. Now I have written a program that estimates the DOA usingmusic>> algorithm. >> There are some queries and doubts about the results I got from theoutput>> which I would like to share. >> Let N be the no of sensors and M be the number of signals incident onthe>> sensors. >> When I do the SVD of the auto correlation matrix, I am supposed to get >> (N-M) number of eigen values which are equal to the variance of noise >> vector. > >That happens only if the number of signals is indeed smaller >than the number of sensors. > >> I am getting very small values which is in concurrence with the >> theory but I am not getting the same values. > >Who said you would get the same values? > >> The noise eigen values are >> decreasing. Also the value of the first eigen value of the signalsubspace>> is relatively very large than the rest of the eigen values of thesignal>> subspace. > >Is there a reason why it shouldn't? > >> Is there an error in my program? > >I have no idea. What you have described so far is more or less >to be expected. > >> Also every time I execute the program, the peaks are varyingenormously>> for the various DOA signals. sometimes some peaks in the plots are verylow>> except the peak corresponding to the first eigen vector. > >Where did you get those peaks from? > >> I plotted the spectrum (doa spectrum) from -90 to +90 degrees. When itry>> to include a DOA nearer to the boundary (-80 to -90) and (+80 - +90),they>> are invariably damped. Can anyone explain the reason for thisbehaviour?> >MUSIC computes no peaks. Whatever it is you plot, it is random >data that are unrelated to anything useful in the signal. > >Rune > >

Reply by ●September 19, 20082008-09-19

On 19 Sep, 21:15, "krish_dsp" <nmkr...@gmail.com> wrote:> hi.. > i will talk about the eigen values first. When I read the theory of MUSIC > vectors, it was given that (in the form of expression) that out of the N > eigen values we get, first M (no of signals) eigen values will be equal to > the sum of the variance of noise and the eigen value of signals, then the > remaining (N-M) eigen values will be equal to the variance of the noise. So > all the N-M values should be equal isn't it. B'cos the auto correlation of > the noise results in (sigma)^2 * I(identity matrix).That's the *expected* result in a perfect world. Once you actually implement something those idealized assumptions break down.> If its not clear, I can share my program as a followup message. > may be I am not explaining the things well. As u said the MUSIC doesn't > compute any peaks. But for visual representation of the working of the > algorithm, i plotted the result.So you say that 1) MUSIC produces no visually relevant result 2) You visualized the result anyway and ask why the visual plot doesn't make sense to you...? Rune

Reply by ●September 19, 20082008-09-19

ok...i think the code I wrote will give you a better picture of what I am trying to tell... here is the code...one has to change the values in the array DOA between -90 and + 90 to get a plot. When u increase the no of signals to more than 2 the results are as I stated in my first mail. Also if u give values between -80 to -90 or +80 to +90, u can see the errors in the final plot. here is the matlab code, i hope it clarifies what I am referring to. close all; clear all; clc; %-------------------------------------------------------------------------- d = 2; % lamda/d is the spacing between the sensors SENSORS = 20; % NO OF SENSORS % DIRECTION OF ARRIVALS IN DEGREES (NO OF DIRECTIONS CAN BE DECREASED OR % INCREASED BY ADDING ANY ANGLE BETWEEN -90 AND +90 IN THE MATRIX DOA DOA = [-20 40]; DOA = pi*DOA / 180; snpshot = 100; % No of samples taken %-------------------------------------------------------------------------- % A LxK MATRIX REPRESENTING THE 100 SNAP SHOTS OF THE SIGNAL INCIDENT ON % THE FIRST SENSOR WHERE L IS THE NUMBER OF DIFFERENT SIGNALS AND K IS THE % NUMBER OF SNAP SHOTS (SIMULATED INPUT) ang = 0 for l = 1:size(DOA,2) ang = ang + 0.23 for k = 1:snpshot signal(l,k) = sin(2*pi*ang*k)*cos(2*pi*(ang+0.1)*k); %100 samples of the signal end end %-------------------------------------------------------------------------- % A LxK MATRIX REPRESENTING THE STEERING VECTOR L REPRESENTS THE NUMBER OF % SENSORS AND K REPRESENTS THE NO OF ARRIVING SIGNALS % CONSIDERING A SPACING OF LAMDA/2 BETWEEN THE SENSORS THE TIME DIFFERENCE % BETWEEN THE WAVES INCIDENT ON THE CONSECUTIVE SENSORS WITH A DOA OF 'THETA' % IS CALCULATED AS LAMDA * SIN(THETA)/(2*c) % THE STEERING VECTOR IS [EXP(-j*2*PI*F*TIMEDELAY)FROM 0 TO SENSORS-1]' strvector(SENSORS, size(DOA,2)) = 0; for k =1:size(DOA,2) for l = 1:SENSORS strvector(l,k) = exp(-j*pi*sin(DOA(k))*(l-1)); end end %-------------------------------------------------------------------------- noise=0.3162/1.414*randn(SENSORS,snpshot); % RANDOM VARIABLE REPRESENTING ADDED NOISE ipsignal = (strvector * signal)+ noise; % X(t) = A(theta) * S(t) + n(t) cov_signal = ipsignal * ipsignal'; % autocorrelation of the matrix cov_signal = cov_signal/snpshot; %Normalization with the number of samples %-------------------------------------------------------------------------- %SINGULAR VALUE DECOMPOSITION FOR FINDING EIGEN VALUES AND VECTORS [u,s,v] = svd(cov_signal); nse_vector = u(:,size(DOA,2):end); % eigen vectors spanning the noise subspace %TESTING THE RESPONSE OF THE ALGORITHM BY PLOTTING A MUSIC SPECTRUM % A BEAM SEARCH VECTOR WHICH IS SAME AS THE STEERING VECTOR ABOVE IS % GENERATED FOR RANGE OF DIRECTIONS -90 DEG TO +90 DEG IS GENERATED WITH % A RESOLUTION OF 0.25 DEG AND THE EIGEN VECTORS OF NOISE SUBSSPACE IS % MULTIPLIED WITH THE BEAM SERCH VECTOR AND THE RECIPROCAL OF THE RESULT % IS PLOTTED angle=-90:0.25:90; %in degrees angle2 = angle *pi/180; % in radians for ctr=1:size(angle,2) beam_serch = exp(-j*pi*sin(angle2(ctr))*[0:SENSORS-1]); denom(ctr) = beam_serch * nse_vector * nse_vector'* beam_serch'; mus_spec(ctr) = abs(1/(denom(ctr))); % MUSIC spectrum end figure; plot(angle,mus_spec); % plotting function %--------------------------------------------------------------------------

Reply by ●September 20, 20082008-09-20

On 20 Sep, 04:08, "krish_dsp" <nmkr...@gmail.com> wrote:> ok...i think the code I wrote will give you a better picture of what I am > trying to tell... > here is the code...one has to change the values in the array DOA between > -90 and + 90 to get a plot. When u increase the no of signals to more than > 2 the results are as I stated in my first mail. Also if u give values > between -80 to -90 or +80 to +90, u can see the errors in the final plot. > > here is the matlab code, i hope it clarifies what I am referring to.No, it doesn't. You are complaining about errors that occur when you attempt to do something that has no chance in hell to produce 'correct' results. This might come as a surprise to you, but it is not sufficient that you (or somebody else) would like to compute or plot a result. There must be a sequence of causes and effects that takes you from whatever you start out from and end up where you want to be. I explained in a post a month ago why this chain of causes and effects break down - you throw away all the information that relates to peaks when you do the MUSIC computations. This is a very simple argument which is totally obvious when you sit down and actually review the equations you implement. Just two problems with that: - You have to sit down and review the equation - You have to understand what you see Rune

Reply by ●October 2, 20082008-10-02